Generation Of The Trigonometric Cubic B-spline Collocation Solutions for the Kuramoto-Sivashinsky(KS) Equation

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ERSOY HEPSON Ö.

International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Thessaloniki, Greece, 25 - 30 September 2017, vol.1978 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1978
  • Doi Number: 10.1063/1.5044169
  • City: Thessaloniki
  • Country: Greece
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

A recent type of B-spline functions, namely trigonometric cubic B-splines, are adapted to the collocation method for the numerical solutions of the Kuramoto-Sivashinsky(KS) equation. Altough Trigonometric Cubic B-spline(TCB) function is continuous derivatives up to order 2, KS equation is splitted into a coupled system of equation including the first and second order derivatives to be able to the TCB collocation method. Crank-Nicolson method is applied for the time integration of the space discretized system resulted by TCB-spline approach. Some initial boundary value problems are solved to show the validity of the proposed method.